A dynamically unbalanced rotor in viscoelastic orthotropic supports equipped with a two-plane automatic ball balancer (ABB) is considered. Based on an analysis of the equations describing the stationary modes of motion of the system, the possibility of the existence of the balanced mode is shown and the necessary conditions for its existence are found. Critical rotor speeds are found for a case of a rotor without an ABB. Amplitude-frequency responses for rotors in isotropic and orthotropic supports are constructed. Autobalancing process for the cases of rotation at constant angular velocity and constant angular acceleration is investigated.